Wow... everyone has been pretty much wrong. The worst of all, however, has to be the "your modem is a router" guy. I'm sorry, dude, but you're completely wrong. A modem is not a router; although it provides traffic forwarding, it's a modulator-demodulator. Comparing a modem to a router is like comparing an oven to a cakepan; the first one can only make the cake, the second one can only deliver it. Modems are responsible for converting the traffic into a more readable format and, although cable modems do not function the same way as traditional modems, they do still serve the traffic in this manner. Your modem will NOT have a routing table because it's not routing anything; if it was routing something, then the modem and computer would have different IP addresses, which they don't. Your computer initiates a DHCP request, which exits through your NIC through your modem to the ISP; the reply comes from the ISP back through the modem to your computer. Your modem does not need an IP address.
Phew. On to the question. Everyone who said "you have to call your ISP" gets half a cookie. Depending on how your ISP handles their DHCP lease cycle, your IP address is likely to change on a regular interval; this is usually 7 to 14 days, although it can be much longer. If you can't wait that long, you'll have to call your ISP and get them to change your IP address.
Of course, I have to concur with the person that asked WHY you need to change your IP address. If it is concerning inbound attacks on your computer, then just call your ISP and explain that. Otherwise, your reason is probably either wrong or ill-founded. If it is because of a perceived "requirement" for anything, then it's just wrong. If it is because of possibly borderline-legal or illegal activities, then it's ill-founded and I can't give you any advice because my morals keep me from doing so. Why would that make it ill-founded? Because if you're naive enough to leave tracks, you deserve to be caught.